Reduced words and a length function for G(e,1,n)

In the first part of this paper we study normal forms of elements of the imprimitive complex reflection group G(e,1,n). This allows to prove a conjecture of Broue on basis elements and the canonical symmetrizing form of the associated cyclotomic Hecke algebra. Secondly we introduce a root system for G(e,1,n) and study the associated length function. This has many properties in common with the usual length function for finite Weyl groups.